An optimal adaptive model-free control with a Kalman-filter-based observer for a generic nonlinear MIMO system

In this paper, a new structure to design an optimal model-free control policy for tracking problem of nonaffine nonlinear multi-input-multi-output (MIMO) systems is proposed. Here, it is assumed that the system dynamics contains bounded unknown nonlinearities and external disturbances. Also, it is assumed that all the states in the system can be measured using a set of sensors, but there is a source of noise on each of the sensors with a white noise model. The design procedure is proposed using online solution of the Hamilton-Jacobi-Bellman equation. The algorithm includes two separate robust adaptive laws for estimating the unknown nonlinear and linear terms. The adaptive law for estimation of the nonlinear terms is a model-free estimation algorithm, since it does not require any regressor parameters. In addition, a Kalman-filter is used to observe the values of the states free of the measurement noises. Moreover, a technique is presented to update the values for controller gain in an online manner. The performance of the proposed algorithm is studied on simulation of the Duffing-Holmes chaotic system with tracking objective.